New orthogonal series approach to state-space analysis of 1-D and 2-D discrete systems

An orthogonal series approach is presented for state-space analysis of 1-D and 2-D linear time-invariant discrete systems. This approach makes use of the backward shift operation matrix derived in the paper, and yields explicit expressions for the state and output orthogonal coefficient matrixes. These expressions involve only multiplication of small dimension matrixes thus simplifying the computational effort as compared to known orthogonal function techniques, where the inversion of large matrixes is required